Atkin-Lehner |
2- 3- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
11952m |
Isogeny class |
Conductor |
11952 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-6691590144 = -1 · 212 · 39 · 83 |
Discriminant |
Eigenvalues |
2- 3- -1 0 -3 -6 4 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7923,271474] |
[a1,a2,a3,a4,a6] |
Generators |
[47:54:1] |
Generators of the group modulo torsion |
j |
-18420660721/2241 |
j-invariant |
L |
4.0166630216887 |
L(r)(E,1)/r! |
Ω |
1.2823183638185 |
Real period |
R |
0.39154307688146 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
747c1 47808bt1 3984f1 |
Quadratic twists by: -4 8 -3 |